Problem: Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N). Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.

First, let q be an empty sequence. Then, perform the following operation until p becomes empty:

* Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.



When p becomes empty, q will be a permutation of (1, 2, ..., N).

Find the lexicographically smallest permutation that can be obtained as q.

Constraints

* N is an even number.
* 2 ≤ N ≤ 2 × 10^5
* p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the lexicographically smallest permutation, with spaces in between.

Examples

Input

4
3 2 4 1


Output

3 1 2 4


Input

2
1 2


Output

1 2


Input

8
4 6 3 2 8 5 7 1


Output

3 1 2 7 4 6 8 5

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define rep(i,a,b) for (int i=(a); i<=int(b); i++)
#define lc (o << 1)
#define rc (o << 1 | 1)
#define mid ((l + r) >> 1)
using namespace std;

const int maxn = 200005;
int p[maxn];
struct SegmentTree {
	int e, mn[maxn<<2];
	void build(int o, int l, int r) {
		if (l == r) { mn[o] = l * 2 - e; return; }
		build(lc, l, mid); build(rc, mid+1, r);
		mn[o] = p[mn[lc]] < p[mn[rc]] ? mn[lc] : mn[rc];
	}
	int query(int o, int l, int r, int x, int y) {
		if (l == x && y == r) return mn[o];
		if (y <= mid) return query(lc, l, mid, x, y);
		if (mid < x) return query(rc, mid+1, r, x, y);
		int L = query(lc, l, mid, x, mid);
		int R = query(rc,  mid+1, r, mid+1, y);
		return p[L] < p[R] ? L : R;
	}
} T[2];
struct node {
	int l, r, p, q, a, b;
	bool operator < (const node &x) const {
		return a > x.a;
	}
} tmp;
priority_queue<node> Q;
int n;

void calc(int l, int r) {
	node res; 
	res.l = l; res.r = r;
	if (l&1) {
		res.p = T[1].query(1, 1, n/2, (l+1)/2, (r+1)/2);
		res.q = T[0].query(1, 1, n/2, (res.p+2)/2, (r+1)/2);
	}
	else {
		res.p = T[0].query(1, 1, n/2, (l+1)/2, r/2);
		//printf("%d\n", res.p);
		res.q = T[1].query(1, 1, n/2, (res.p+2)/2, (r+1)/2);
	}
	res.a = p[res.p]; res.b = p[res.q];
	Q.push(res);
}

int main() {
	scanf("%d", &n);
	T[0].e = 0; T[1].e = 1;
	rep (i, 1, n) scanf("%d", &p[i]);
	T[0].build(1, 1, n/2);
	T[1].build(1, 1, n/2);
	calc(1, n);
	while (!Q.empty()) {
		tmp = Q.top(); Q.pop();
		printf("%d %d ", tmp.a, tmp.b);
		if (tmp.l < tmp.p) calc(tmp.l, tmp.p-1);
		if (tmp.p + 1 < tmp.q) calc(tmp.p+1, tmp.q-1);
		if (tmp.q < tmp.r) calc(tmp.q+1, tmp.r);
	}
	return 0;
}